| Summary: | By analogy with the Makkai duality for first order logic, we develop a duality theory for $ kappa$-exact categories in which the structure on the model categories is that induced by $ kappa$-reduced products. The main theorem, a strong completeness result, states that for any small $ kappa$-exact category $F$, the functor $F { buildrel{e sb F} over longrightarrow} hom({ bf Mod}F,{ bf Sets})$ defined by evaluation is an equivalence of categories, where $hom({ bf Mod}F,{ bf Sets})$ is the category of functors from ${ bf Mod}F$ to Sets which preserve the reduced product structure.
|
|---|
